I guess then that there is also no
"check status with script /etc/init.d/serviceX"

or something similar and then I could hide some script in serviceX
which returns some result code that monit can interpret as ok or
failure and start some actions accordingly.

You guess correct. However, many have requested such a feature over
the years and I think it is something we need to implement. What do
others think?

Interesting, I've been using Monit now for a total of 48 hours and it
was the first thing I looked for in the documentation and was surprised
not to find it. I guess it all wraps up in what monit is trying to do
which is be as easy as possible to setup and configure. However to me
having custom scripts would be welcome.